Six-Dimensional Spatial Dimension Chain Modeling via Transfer Matrix Method with Coupled Form Error Distributions - Lu Liu; Xin Jin; Huan Guo; Chaojiang Li (Machines)
In tolerance design for complex mechanical systems, 3D dimension chain analyses are crucial for assembly accuracy. The current methods (e.g., worst-case analysis, statistical tolerance analysis) face limitations from oversimplified assumptions—treating datum features as ideal geometries while ignoring manufacturing-induced spatial distribution of form errors and failing to characterize 3D coupled error constraints. This study proposes a six-dimensional spatial dimension chain (SDC) model based on transfer matrix theory. The key innovations include (1) a six-dimensional model integrating position and orientation vectors, incorporating geometric error propagation constraints for high-fidelity error prediction and tolerance optimization, (2) the characterization of spatially distributed form errors and 3D coupled errors of spatial dimension chain-based multiple mating-surface constraint (SDC-MMSC) using six-degree-of-freedom (6-DoF) geometric error components, reducing the assembly topology complexity while improving the efficiency, and (3) a 6-DoF error characterization method for non-mating-constrained data, providing the theoretical basis for SDC modeling. The experimental validation on an aero-engine casing assembly shows that the SDC model captures multidimensional closed-loop spatial errors, with absolute errors of max–min closed-loop distances below 9.3 μm and coaxiality prediction errors under 8.3%. The SDC-MMSC method demonstrates superiority, yielding normal vector angular errors <0.008° and envelope surface RMSE values <0.006 mm. This method overcomes traditional simplified assumptions, establishing a high-precision, multidimensional distributed-form-error-driven SDC model for complex mechanical systems.